If you think in a "neolatin alphabet", normativizing letter use (like, "ch" always for /tS/ sound, "sh" always for /S/, etc.), it's plausible but not desired. The alphabet would lose flexibility, we would need to abuse digraphs or create about 20 new graphemes...

If you think in something far more radical - writing all of them as one language, it's just making a Vulgar Latin orthography, really . It's more plausible, however, defeats the very reason to use an alphabet: phoneme-grapheme correlation.

sölvm magnvm homö potest esse quandö rëses nvnqvam prae vïdërunt creat.(A human being can only be great when creat what was never seen before.)